K-means Clustering in Python

Generate a dataset

set.seed(505)
f1 =c(runif(150,-20,30),runif(150,15,65),runif(150,50,100),runif(200,-20,100))
f2 =c(runif(150,-10,30),runif(150,40,80),runif(150,-30,10),runif(200,-35,100))
df=data.frame('x'=f1,'y'=f2)
# plotting
plot(f1, f2,cex=0.5,pch=19,main="orginal", col='darkgrey')

Choose Number of clusters: K

# Number of clusters
k = 3
# setup color for plotting
colors = RColorBrewer::brewer.pal(n = k, name = 'Paired')

Random select K points as Intial Centroids

# intial X coordinates of random centroids
index_centriods =  sample(1:nrow(df),k)
intial_Centroids = df[index_centriods,]

# Plotting along with the Centroids
plot(f1, f2, col='darkgrey',cex=0.5,pch=19,ylab='y',xlab='x',main="Intial Centroids ")
points(x=intial_Centroids$x, y=intial_Centroids$y,cex=1.5,pch=23,col='red')

Creat function for assigning the points to K clusters

# assign the points to 3 clusters
assignment=function(df, centroids,k,iter,colors){
   # creating new cols for computing euclidean distance to the centroids point
    for (i in 1:k){
        # euclidean distance = sqrt((x1 - x2)^2 - (y1 - y2)^2)
        df[paste('Distance_from_',toString(i),sep='')] = 
            sqrt((df$x- centroids[i,1]) ** 2+
                   (df$y - centroids[i,2]) ** 2)}

    # creating a new col for shows the closest centroids
    df['closest'] = apply(df[2+1:k],1,FUN=function(x) which(x==min(x))[1])
    # creating a new col for shows the color
    df['color']  = apply(df['closest'],1,FUN = function(x) colors[x])
    plot(df$x,df$y,col=df$color,cex=0.5,pch=19,ylab='y',xlab='x',main=paste('Clustering:',iter))
    points(x=centroids$x, y=centroids$y,cex=1.5,pch=23,col='red')
    return (df)
  }
  1. Compute the distance between the points and each centroids (Distance_from_i)
  2. Identify the closet centroids of each point (closest)
  3. Split the points to K clusters
Centroids = intial_Centroids
df= assignment(df,Centroids,k,1,colors)

head(df)
##            x         y Distance_from_1 Distance_from_2 Distance_from_3
## 1 -13.444819  4.463472        94.67149        82.79937        87.28534
## 2   5.197805 26.989491        71.67655        77.32320        58.64648
## 3 -15.004434 14.828633        84.63812        88.08710        82.15963
## 4 -15.463153 17.912041        81.67425        89.83152        80.83027
## 5 -18.964604  7.478121        92.57031        89.00012        89.67948
## 6  19.279155 -5.429700       105.82957        48.64243        74.82356
##   closest   color
## 1       2 #1F78B4
## 2       3 #B2DF8A
## 3       3 #B2DF8A
## 4       3 #B2DF8A
## 5       2 #1F78B4
## 6       2 #1F78B4
# ploting first cluster result

Creat function for updating the centroids

The new centroids are the means of each cluster

# function for update centroids
update= function(centroids,k,df){
    for (i in 1:k){
        centroids[i,1] = mean(df[df$closest==i,]$x)
        centroids[i,2] = mean(df[df$closest==i,]$y)}
    plot(df$x,df$y,col=df$color,cex=0.5,pch=19,ylab='y',xlab='x',main="New centroids ")
    points(x=centroids$x, y=centroids$y,cex=1.5,pch=23,col='red')
    return (centroids)}
Centroids = update(Centroids,k,df)

### Cluster the data with new centroids

# run the second clustering 
df= assignment(df,Centroids,k,2,colors)

# updat the centroids again 
Centroids = update(Centroids,k,df)

# run the third clustering 
df= assignment(df,Centroids,k,3,colors)

# updat the centroids again
Centroids = update(Centroids,k,df)

# run the fourth clustering 
df= assignment(df,Centroids,k,4,colors)

Centroids = update(Centroids,k,df)

# run the fifth clustering 
df= assignment(df,Centroids,k,5,colors)

Centroids = update(Centroids,k,df)

Now we get 3 clear clusters

Create a function for the whole K-means process.

# df = dataset 
# iteration = nunmber of iteration 
# k =number of cluster 
Kmean_2D= function(df, k,iteration){
  # plot the Orginal dataset
  plot(df$x, df$y,cex=0.5,pch=19,main="Orginal df")
  # setup color
  colors = RColorBrewer::brewer.pal(n = k, name = 'Paired')
  # initial X coordinates of random centroids
  index_centriods =  sample(1:nrow(df),k)
  intial_Centroids = df[index_centriods,]
  # ploting the initial centroids
  plot(df$x, df$y,cex=0.5,pch=19,main="Orginal df")
  points(x=intial_Centroids$x, y=intial_Centroids$y,cex=1.5,pch=23,col='red')
  
  Centroids = intial_Centroids
  for (iter in 1:iteration){
    df= assignment(df,Centroids,k,iter,colors)
    if (iter!=iteration){
    Centroids = update(Centroids,k,df)}
    }
}

Try on a new dataset

set.seed(505)
f1 =c(runif(150,-20,30),runif(150,15,65),runif(150,50,100),runif(150,80,120),runif(200,-20,100))
f2 =c(runif(150,-10,30),runif(150,40,80),runif(150,-30,10),runif(150,30,80),runif(200,-35,100))
df=data.frame('x'=f1,'y'=f2)
Kmean_2D(df,k=4,6)